10 Find the length of the hypotenuse to the nearest hundredth.Check It Out: Example 1AFind the length of the hypotenuse to the nearest hundredth.57ca2 + b2 = c2Pythagorean Theorem= c2Substitute for a and b.= c2Simplify powers.74 = cSolve for c; c = c2.8.60  c

11 Find the length of the hypotenuse to the nearest hundredth.Check It Out: Example 1BFind the length of the hypotenuse to the nearest hundredth.triangle with coordinates (–2, –2), (–2, 4), and (3, –2)xy(–2, 4)The points form a right triangle.a2 + b2 = c2Pythagorean Theorem= c2Substitute for a and b.= c2Simplify powers.(–2, –2)(3, –2)61 = cSolve for c; c = c2.7.81  c

12 Additional Example 2: Finding the Length of a Leg in a Right TriangleSolve for the unknown side in the right triangle to the nearest tenth.a2 + b2 = c2Pythagorean Theorem25b72 + b2 = 252Substitute for a and c.49 + b2 = 625Simplify powers.– –49Subtract 49 from each side.b2 = 5767b = 24Find the positive square root

13 Check It Out: Example 2Solve for the unknown side in the right triangle to the nearest tenth.a2 + b2 = c2Pythagorean Theorem12b42 + b2 = 122Substitute for a and c.16 + b2 = 144Simplify powers.– –16Subtract 16 from both sides.4b2 = 128b  11.31Find the positive square root.

14 Additional Example 3: Using the Pythagorean Theorem for MeasurementTwo airplanes leave the same airport at the same time. The first plane flies to a landing strip 350 miles south, while the other plane flies to an airport 725 miles west. How far apart are the two planes after they land?a2 + b2 = c2Pythagorean Theorem= c2Substitute for a and b.122, ,625 = c2Simplify powers.648,125 = c2Add.805 ≈ cFind the positive square root.The two planes are approximately 805 miles apart.

15 Check It Out: Example 3Two birds leave the same spot at the same time. The first bird flies to his nest 11 miles south, while the other bird flies to his nest 7 miles west. How far apart are the two birds after they reach their nests?a2 + b2 = c2Pythagorean Theorem= c2Substitute for a and b.= c2Simplify powers.170 = c2Add.13 ≈ cFind the positive square root.The two birds are approximately 13 miles apart.

16 Lesson QuizUse the figure for Problems 1 and 2.1. Find the height h of the triangle.8 m2. Find the length of side c to the nearest meter.10 mch12 m3. An escalator in a shopping mall is 40 ft long and 32 ft tall. What distance does the escalator carry shoppers?6 m9 m2624 ≈ 51 ft